International Journal of Nonlinear Analysis and Applications

Investigation of a nonlocal Stieltjes type coupled boundary value problem of higher order nonlinear ordinary differential equations

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics and Systems Engineering Florida Institute of Technology Melbourne, FL 32901, USA

2 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Abstract

We explore the existence criteria for solutions of a coupled system of two higher-order nonlinear ordinary differential equations supplemented with nonlocal and Stieltjes-type coupled boundary conditions. Such problems are useful in view of their occurrence in certain physical phenomena (see  Section 1). In our first result, we apply the Leray-Schauder alternative to establish the existence of solutions to the given problem, while the second result deals with the uniqueness of solutions for the problem at hand, and it is based on Banach's fixed-point theorem.  Examples are included to illustrate the results obtained. Finally, we indicate some new results arising as special cases of the ones presented in this paper.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 28 June 2025
  • Receive Date: 01 November 2024
  • Revise Date: 03 January 2025
  • Accept Date: 04 January 2025